Television images showed Tarkowski elbow Brighton forward Glenn Murray in the ribs and he was charged with violent conduct by the Football Association.
Burnley said that the player had accepted the charge but argued that the suspension was excessive. However, that appeal was rejected by an Independent Regulatory Commission.
Tarkowski misses this weekend's game at Turf Moor against Tottenham Hotspur, the Boxing Day game at Manchester United and the trip to Huddersfield Town on December 30.
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